Application of Persistent Homology in Forecasting Realized Volatility

This paper proposes a novel algorithm called Persistent Homology for Realized Volatility (PHRV), which aims to effectively incorporate persistent homology (PH) into neural network models to increase their forecast accuracy in predicting realized volatility (RV). This paper also proposes a novel neural network model for multi-step forecasting that systematically yields statistically significanlty more accurate forecasts than other forecasting models. The proposed model coined as NBEATSx-VP utilizes neural basis expansion analysis with exogenous variables (NBEATSx) network, and VIX close prices and 2-dimensional Wasserstein distances of stock log returns as exogenous variables. While considering Root-Mean-Square Error (RMSE), NBEATSx-VP demonstrates a minimum 9% improvement in forecast precision compared to benchmark models. Considering Quasi-likelihood (QLIKE), on the other hand, NBEATSx-VP achieves at least 13% more accurate forecasts than state-of-the-art models